Without direct evidence/eye witness reports, an argument could certainly be proved by circumstantial evidence, and that is what the State is trying to do.
The problem is, it takes several pieces of circumstantial evidence to really prove something (usually) and the State doesn't seem to have the evidence.
If they had witnesses hearing an argument between a man and woman and could identify it as coming from Oscar's house, or if they had text messages that indicated that an argument was going on, that would go a long way towards proving an argument by circumstantial evidence. All the state has though is one witness who heard a woman's voice talking loudly - maybe arguing - but she couldn't hear the other side and couldn't identify it as coming from Oscar's house.
The other way they could come closer to proving that there was an argument leading up to the shooting is if they can prove that Oscar's version could not have possibly happened. That's what I'm waiting for - to see if they can really undermine his account.